Probability model of fully non-stationary ground motion with the target response spectrum compatible
LIU Zhangjun1,2,LIU Zenghui1,LIU Wei1
1. College of Civil Engineering & Architecture,China Three Gorges University,Yichang 443002,China;
2. Hubei Key Laboratory of Disaster Prevention and Reduction,China Three Gorges University,Yichang 443002,China
Abstract：Based on the intensity modulation function,a class of extended time-frequency modulation function for non-stationary ground motion was developed. In conjunction with the power spectral density function of stationary earthquake processes,an evolutionary power spectra model of fully non-stationary ground motion was established. The values of the model parameters were determined according to the Chinese code for seismic design of buildings. Applying the simulation method of hybrid spectral representation and random function for non-stationary stochastic processes,a complete set of representative seismic time-histories with assigned probabilities was obtained,and the average response spectrum of representative seismic time-histories was determined accordingly. In order to ensure the calculated average response spectrum to be in agreement with the design response spectrum,the average relative error and the maximum relative error were suggested to control the tolerance between the two response spectrums. The agreement was realized through three times iterative corrections for the evolutionary power spectra. The study provides a basis for the application of stochastic dynamics of structures in engineering practices.
刘章军1,2，刘增辉1，刘威1. 全非平稳地震动过程的概率模型及反应谱拟合[J]. 振动与冲击, 2017, 36(2): 32-38.
LIU Zhangjun1,2,LIU Zenghui1,LIU Wei1. Probability model of fully non-stationary ground motion with the target response spectrum compatible. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(2): 32-38.
[1] 欧进萍, 牛荻涛, 杜修力. 设计用随机地震动的模型及其参数确定[J]. 地震工程与工程振动, 1991, 11(3): 45–54.
OU Jinping, NIU Ditao, DU Xiuli. Random earthquake ground motion model and its parameter determination used in aseismic design [J]. Earthquake Engineering and Engineering Vibration, 1991, 11(3): 45–54.
[2] Yeh C H, Wen Y K. Modeling of nonstationary ground motion and analysis of inelastic structural response [J]. Structural Safety, 1990, 8: 281–298.
[3] Wang J, Fan L, Qian S, Zhou J. Simulations of non-stationary frequency content and its importance to seismic assessment of structures [J]. Earthquake Engineering and Structural Dynamics, 2002, 31:993–1005.
[4] 刘章军, 王磊, 但庆文, 等. 非平稳地震动的广义演变谱模型及在水工抗震中的应用[J]. 水利学报, 2015, 46(9): 1028–1036.
LIU Zhangjun, WANG Lei, DAN Qingwen, et al. Generalized evolutionary spectrum of non-stationary ground motion and its applications in seismic design of hydraulic structures [J]. Journal of Hydraulic Engineering, 2015, 46(9): 1028–1036.
[5] 杨庆山, 田玉基. 地震地面运动及其人工合成[M]. 北京: 科学出版社, 2014.
YANG Qingshan, TIAN Yuji. Earthquake ground motions and artificial generation [M]. Beijing: Science press, 2014.
[6] 张郁山, 赵凤新. 基于小波函数的地震动反应谱拟合方法[J]. 土木工程学报, 2014, 47(1): 70–81.
ZHANG Yushan, ZHAO Fengxin. Matching method of ground-motion response spectrum based on the wavelet function [J]. China Civil Engineering Journal, 2014, 47(1): 70–81.
[7] Cacciola P. A stochastic approach for generating spectrum compatible fully nonstationary earthquakes[J]. Computers and Structures, 2010, 88: 889–901.
[8] Li J, Chen J B. Stochastic dynamics of structures [M]. Singapore: John Wiley & Sons Pte Ltd, 2009.
[9] 王鼎, 李杰. 工程地震动的物理随机函数模型[J]. 中国科学: 技术科学, 2011, 41(3): 356–364.
WANG D, LI J. Physical random function model of ground motions for engineering purposes [J]. Science China Technological Sciences, 2011, 54(1): 175–182.
[10] 李杰, 王鼎. 工程随机地震动物理模型的参数统计与检验[J]. 地震工程与工程振动, 2013, 33(4): 81–88.
LI Jie, WANG Ding. Parametric statistic and certification of physical stochastic model of seismic ground motion for engineering purposes [J]. Journal of Earthquake Engineering and Engineering Vibration, 2013, 33(4): 81–88.
[11] 刘章军, 曾波, 周宜红, 等. 地震动过程的概率模型及在重力坝抗震可靠度分析中的应用[J]. 水利学报, 2014, 45(9): 1066–1074.
LIU Zhangjun, ZENG Bo, ZHOU Yihong, et al. Probabilistic model of ground motion processes and seismic dynamic reliability analysis of the gravity dam [J]. Journal of Hydraulic Engineering, 2014, 45(9): 1066–1074.
[12] 刘章军, 曾波, 吴林强. 非平稳地震动过程模拟的谱表示-随机函数方法[J]. 振动工程学报, 2015, 28(3): 411–417.
LIU Zhangjun, ZENG Bo, WU Linqiang. Simulation of non-stationary ground motion by spectral representation and random functions [J]. Journal of Vibration Engineering, 2015, 28(3): 411–417.
[13] GB50011-2010. 建筑抗震设计规范[S]. 北京: 中国建筑工业出版社, 2010.
GB50011-2010. Code for seismic design of buildings [S]. Beijing: China Architecture & Building Press, 2010.
[14] 薛素铎, 王雪生, 曹资. 基于新抗震规范的地震动随机模型参数研究[J]. 土木工程学报, 2003, 36(5): 5–10.
XUE Suduo, WANG Xuesheng, CAO Zi. Parameters study on seismic random model based on the new seismic code [J]. China Civil Engineering Journal, 2003, 36(5): 5–10.
[15] Liu Zhangjun, Liu Wei, Peng Yongbo. Random function based spectral representation of estationary and Non-stationary Stochastic Processes [J]. Probabilistic Engineering Mechanics, doi: 10.1016/j. probengmech. 2016. 04. 004.
[16] 刘章军, 方兴. 平稳地震动过程的随机函数-谱表示模拟[J]. 振动与冲击, 2013, 32(24): 6–10.
LIU Zhangjun, FANG Xing. Simulation of stationary ground motion with random functions and spectral representation [J]. Journal of Vibration and Shock, 2013, 32(24): 6–10.
[17] Shinozuka M, Sato Y. Simulation of nonstationary random processes [J]. Journal of Engineering Mechanics Division, ASCE, 1967, 93(1): 11–40.
[18] Deodatis G, Shinozuka M. Simulation of seismic ground motion using stochastic waves [J]. Journal of Engineering Mechanics, 1989, 115(12): 2723–2736.
[19] Clough R W, Penzien J. Dynamics of Structures [M]. McGraw-Hill, New York, 1975.
